Is this an unreasonable request? (Girlfriends past fling)

My girlfriend's past fling has been consistently trying to contact her. He texts/calls her often but she blatantly ignores him and never responds. This is enough for me and I wouldn't go as far as to ask her to change her phone number.

This guy doesn't seem to take a hint though. He's been migrating toward Facebook where he's been consistently commenting on her pictures/status updates. The thing is, he doesn't comment like normal people, but prefers to use poetry! Personally I interpret 95% of the things he writes as romantic longing for my girlfriend, although sometimes it's vague. However, he has also sent her private poetry via Facebook, which she has shown me, that is blatant and to the point. It's pretty obvious he wants my girlfriend.

I don't feel threatened at all. We have been dating for nearly a year, we are totally committed to each other and in love. Normally I'm not needy/insecure but every time I look at my girlfriend's profile I see this guy's nonsense. Is it wrong for me to ask her to block him entirely on the site?